I've seen a few people saying that poets can't be writers, and writers can't be poets.

I can't speak for anyone else, but in my book, the two go hand and hand. If you write any sort of material, you're a 'writer'. If you've published an essay, you're a writer. Written a novel? You're a writer. Finished a book of poetry? Yep, you're still a writer.

Authors of fiction and/or essays can also be poets. Just because you usually write Fantasy, for example, that doesn't mean you can't learn to write a poem. Poetry is, honestly, a lot easier to write than fiction. You can fly by the seat of your pants when working on a poem, making up the form as you go.

Anyone can create any genre or type of writing if they're willing to learn, and have the passion to stick with it.